# Modality and open future

I've been thinking what open future (OF) views can say about the modality of statements about the future. There are two OF semantics, which I'll call N and F. Suppose Curley now exists, and that Curley's freely taking the bribe is open. On the N semantics, Curley will freely take the bribe is neither true nor false. On the F semantics, it is false that Curley will freely take the bribe. The N semantics requires denial of excluded middle. The F semantics requires denial of the principle that, basically, not(will(p)) iff will(not(p)).

Suppose now that we say that a proposition p possibly/necessarily/impossibly is V iff p is V in some/all/no worlds, where V is a truth value or a logical combination of truth values like "neither true nor false", which I will abbreviate "ntnf". Let p be the proposition that Curley will freely take the bribe. On the F semantics, p is false in every world. For in some worlds Curley's freely taking the bribe is open, and in those worlds p is false by that semantics. And in all other worlds, it is determined that Curley won't freely take the bribe (e.g., because it is determined that there is no Curley, or that nobody will ever offer Curley a bribe, or whatever). So, in every world, p is false, and so p is necessarily false.

On the N semantics, things are more interesting. In worlds where Curley's freely taking the bribe is open, p is ntnf. In worlds where Curley's freely taking the bribe is not open, p is false. Therefore, on the N semantics, p is possibly ntnf and possibly false, and necessarily not true.

So what's wrong with this? Well, one thing is that as Geoff Pynn pointed out in the previous discussion of open futurism, the open futurist surely wants to say that p is a "future contingent". But if p is necessarily false, as it is on the F semantics, then that's endangered. And if p is necessarily not true, then it's also in a bit of trouble.

On might think this is not a problem for the N semantics. After all, we do have contingency: it is contingent that p is ntnf, since in some worlds p is not ntnf but false. But this is not the kind of contingency in virtue of which we say that p is a "future contingent". Here's one way to see this. Suppose q is some kind of a weird paradoxical proposition that is necessarily ntnf (I don't think there are such, since myself I accept classical logic; but the N-semanticist won't be credible in saying this) and that has no contingency in it (think of liar sentences and the like; or maybe think of vague modal claims, such as that necessarily anybody with 100 hairs is bald). Now, let r be the proposition q & h, where h is the proposition that there are horses. Then, r is ntnf in those worlds in which there are horses, and is false in those worlds in which there are no horses. (I take it that the conjunction of an ntnf proposition with a false one is false.) So r has exactly the same kind of contingency that p does. But when we call p a contingent, we don't mean to make p be like r, an unfortunate proposition which in some worlds just manages to rise to the level of ntnf, while being simply false in all the others.

Here's another way to see that the kind of contingency we get is not the right kind of contingency. Suppose God is a necessary being and is in time, and let s be the proposition that God will freely create a prime number of angels in the future. Then in most worlds, s is ntnf. In some worlds, s may be false, say because in those worlds God has promised something entailing that he won't create a prime number of angels in the future. So s has a contingency: in some worlds it's false and in others it's ntnf. But this contingency tracks not the contingency in God's choice how many angels to create in the future, but rather it tracks the contingency in what God promises. And that's the wrong contingency to track. The contingency in s is about the past, while what we want to explain is why s is a future contingent.

Suppose the above is right. Then when we think about open futurism, we think about propositions like p (about Curley) and s (about God). If we find open futurism plausible, we see a kind of contingency or openness in what these propositions claim. So we are drawn to open future views. But then the F theorist comes and tells us that we were wrong to think there was openness there--in fact, the proposition p that led us to open futurism is necessarily false, just like the proposition that 2+2=5. In doing so, the F theorist undercuts the basis of the intuitions that drew us to open futurism in the first place. The N theorist is more subtle, but I think in the end does the same thing. We initially thought there was something possible about p and s--that they described how things might be. But they don't. The closest to truth that p and s can rise is being ntnf. Their contingency is a contingency of varying in truth value between ntnf and falsity. But if a proposition is necessarily either ntnf or false, how is it that we initially started off with a pretty clear picture of what it would be like for Curley in the future to freely take a bribe or for God to create a prime number of angels, a picture that then led us to open futurism? The N theorist also cuts down the intuition that led to open futurism.

All the above is predicated on the assumption that the modal status of p depends on p's truth value in different worlds. One might try to work out an alternate account of the modal status of propositions. Here's one approach that has some hope of working. Allow what time it is to differ between possible worlds (this is a somewhat more ontologically commitive version of talking about temporally centered worlds). Thus, in the actual world, it's 10:02 am, but in some possible world it's already noon. Then, in the actual world, p is ntnf (N semantics) or false (F semantics). But there is a world where it's already noon and Curley is freely accepting a bribe. The proposition p is false or ntnf at that world (since at that world, p says that Curley will freely accept a bribe after noon). But there is an updating of p that is true at that world.

To do this rigorously, we need an updating operator, as I mentioned in a comment on the earlier thread, which given a proposition p and a time-difference delta, generates a proposition U(p,delta). It's hard to give a precise account of U. But in some cases, it's pretty easy. Thus, U(that Curley will freely accept a bribe, t), where t is positive, is the proposition that Curley freely accepted a bribe over the last t (units of time) or is freely accepting a bribe or will freely accept a bribe. We also need an operator T which assigns to each world the time which it is at that world.

The semantics now is: possibly(P is V) holds at w0 iff there is a w such that U(p,T(w)-T(w0)) is V at w; necessarily(P is V) holds at w0 iff at every world w, U(p,T(w)-T(w0)) is V at w. Assuming U can be defined, and assuming we're willing to live with a worlds at which it is a time other than the actual world's present, this semantics has the right results. Thus, possibly(it is true that Curley will freely accept a bribe). Likewise, possibly(it is false that Curley will freely accept a bribe). Moreover, both claims hold on both F and N semantics. On the N semantics, we further have: possibly(it is ntnf that Curley will freely accept a bribe).

I do not know how plausible this modal semantics is. In particular, I do not know how comfortable the open futurist will be with the idea that at every time, we are in a different world, since right now I am in a world where it's 10:16, and in four minutes I'll be in a world where it's 10:20. But the latter claim is one I think all A-theorists have to make.

Anyway, so it seems that the open futurist can get out of the modal argument. Fortunately for me, there are other, more serious problems with open futurism. :-)

The N semantics requires denial of excluded middle.

Hey, I thought a feature of N (and an advantage of it over F) is precisely that it lets one keep excluded middle, when developed a certain way: Disjunctions like "He will or he won't" all come out true: "He will" is ntnf, because it's true at some causally possible futures but false at others; same for "He won't"; but "He will or he won't" and the like are true b/c true at all causally possible futures. Or so I thought.

It's really a choice between bivalence and excluded middle. I mean it's a choice between those two given symmetry -- given that you're going to say the same thing about the truth-value of *He will* and *He won't*. (Those who believe in a "thin red line" that makes one of them true & the other false don't have to choose between bivalence & e.m.) If you hang on to bivalence, and so you assign a truth value to both of them, then that truth value has to be False -- nobody wants to say that *He will* and *He won't* are both true. But if they're both False, you can't get excluded middle: if both disjuncts are false, the disjunction can't be true. But if you reject bivalence, you can say the same thing about both of them, saying they're both ntnf, and can get the disjunction to be true on supervaluational grounds.

(This is all the analogue of Stalnaker vs. Lewis on conditional excluded middle vs. bivalence for counterfactuals. What to say about cases where there isn't a single closest A-world, but several closest A-worlds, in some of which C is true, and in others of which C is false? Lewis hangs on to bivalence, and says A->C and A->~C are both false. But then (A->C)v(A->~C) is false, and c.e.m. fails. Stalnaker denies bivalence, and says A->C and A->~C are both ntnf. But then (A->C)v(A->~C) can be true, and c.e.m. is upheld.)

Right, your (1) looks like poison to my open-futurist eyes. That's the kind of thing I'm allergic to. Your (4) also looks like something I'll want to deny. What I'll accept is a "semanticized" version of it:

(4s) If it's true that Curley will take the bribe, then Curley is not free with respect of taking the bribe.

Here's how I was inclined to judge various disjunctions and conditionals. I wrote these up some years ago (for students), but they still look right to me. (Though I wouldn't be too surprised if I'm making some mistakes.)

T 1D. Either I will or I won't (eat Cheerios for
breakfast tomorrow)
F 2D. If I will, then it's inevitable that I will
F 3D. If I won't, then it's inevitable that I won't

F 1S. Either it's true that I will or it's true that
I won't
T 2S. If it's true that I will, then it's inevitable
that I will
T 3S. If it's true that I won't, then it's
inevitable that I won't

F 1S'. Either it's true that I will or it's false
that I will
T 3S'. If it's false that I will, then it's
inevitable that I won't

T 1S''. Either it's true that I will or it's not true
that I will
F 3S''. If it's not true that I will, it's inevitable
that I won't

T 1SF. Either it will be true that I did, or it will
be true that I didn't
F 2SF. If it will be true that I did, then it's
inevitable that I will
F 3SF. If it will be true that I didn't, then it's
inevitable that I won't

T 1SF'. Either it will be true that I did, or it will
be false that I did
F 3SF'. If it will be false that I did, then it's
inevitable that I won't

Hi Alex,

I don't seeing that F semantics (which I endorse) has a problem here.

On that semantics your p = "Curley will freely take the bribe" is indeed necessarily false; indeed, it turns out to be a contradiction in terms since 'will' and 'freely' cancel each other out. Against this you say "the open futurist surely wants to say that p is a 'future contingent'." But why would I want to say that? On my view p is not a future contingent at all.

You argue then that my view "undercuts the basis of the intuitions that drew us to open futurism in the first place" by treating future contingents as though they weren't. But that's a mistake. Just because I reject your p doesn't mean that I don't have a way of accommodating intuitions about future contingency. Instead of talking about propositions, I prefer to speak of future contingent states-of-affairs. So in place of p, I put q = "Curley's freely taking the bribe (at future time t*)". Given Curley's being free in the relevant respects, it can't be that q's obtaining is now-inevitable, nor can it be that q's obtaining is now-impossible. Hence, q is a future contingent. It might come about that q obtains and it might not. (Those are non-epistemic 'mights'.)

"I do not know how comfortable the open futurist will be with the idea that at every time, we are in a different world."

I can't speak for all open futurists here, but I for one am comfortable that idea. A-theorists in general should, I think, accept it. And open futurists should be A-theorists.

Alex:

What you're missing is the way in which modality and tense interact on my view.

On an F semantics, as you call it, the future-tense 'will' has modal force. It connotes now-inevitability. On that reading, "Curley will freely take a bribe" is necessarily false.

When expressing future contingency, however, one shouldn't use the future-tense inside the relevant proposition. The issue is whether it is now-inevitable that "Curley freely takes (present tense) a bribe" comes to be true in the future, not whether "Curley will freely (future tense) take a bribe" is true now.

It can be now-possible (not now-inevitable) that "Curley freely takes a bribe in the future" without it being now-possible that "Curley will freely take a bribe in the future".

Do you have F semantics for a-type claims as well? From your remarks, the answer seems negative. (Otherwise, (a) would be necessarily false.) So do you have N semantics for them? And if so, do you reject bivalence or excluded middle for those claims? Or do you have ordinary eternalist semantics for them?

Good questions, Alex. I'm not quite sure what you mean by an "ordinary eternalist semantics", but I think that's the kind of semantics I would give for a-type claims. More exactly, I take (a) to be true iff there exists simpliciter 'Curley's freely taking a bribe in the future', and false otherwise. So on an eternalist ontology (a) comes out as true if at the appropriate time Curley freely takes the bribe, but on a presentist or open future ontology (a) is false until Curley actually freely takes the bribe.

My disagreement with the eternalist over a-type claims is, I take it, not semantic but metaphysical. We can assign different truth values to a-type claims precisely because we disagree about whether truthmakers for those claims exist.

Sorry to have tuned out, Alex -- Just a sudden crush of busy-ness. I'm not sure I'm understanding your modal worry correctly. I think the sense in which "future contingents" are being said to be "contingent" is that there are causally possible (or something like that: terminology varies) futures in which they're true & also causally possible futures in which they're false. The open futurist -- or at least the OF of my basic stripe -- says that in such cases the future-directed propositions in question are ntnf. That doesn't sound like the kind of thing which will itself be a contingent truth, so I guess I'm inclined toward these:

It's metaphysically necessary that if p is a FC [where this is spelled out as above, in terms of causal possibility] at t, then p is ntnf at t

It's metaphysically impossible that p is a FC at t, but is either true or false at t.

*Keith will shovel his driveway Monday afternoon* is now a FC. But the "semanticized" version of it, *It is true [now: 11:38 am Monday morning] that Keith will shovel his driveway Monday afternoon*, is not a FC: there are no causally possible futures (relative to now) at which it is now true that I shovel on Monday afternoon. It's now inevitable that the latter "semanticized" proposition is true, but it's not now inevitable that I will shovel -- or that I won't (no matter what my wife says).

I'm not sure how well that responds to your modal worry.

There's a lot of terminology that can be moving around. I construe propositions as having times built into them. If you think of *Keith is wearing a hat* as something that is true at some times and false at others, then I won't count it as a proposition, but as a "proposition frame" (or whatever terminology one wants to use here). *Keith is wearing a hat at 11:53 am, March 2, 2009* is a proposition (and may be what's expressed now by the sentence "Keith is wearing a hat"), as is *Keith is wearing a hat at some time on March 2, 2009*. I don't know how many others I speak for, but when thinking of propositions in such terms, I don't believe they can switch truth-values (they can't change from true to false or from false to true), or lose truth-values, but they can gain a truth value: they can go from ntnf to True or from ntnf to False.

Keith:

The last paragraph is really interesting. I had once concluded that A-theorists have to think propositions are tensed (i.e., are proposition frames) if they are to distinguish their view from the B-theory. But maybe open future lets one do it differently? Given an open future, one can just stipulate that "now" refers to dthe infimum of the set of times at which there is something open (however one formulates that).

That won't work if there are possible worlds where determinism holds, unless one implausibly says that in our world we have A-theory but in those we'd have to have B-theory. But an open futurist theist might deny that there are any possible worlds where determinism holds. (After all, isn't God always free to work miracles? It's true that God could promise not to do that, but, maybe, promises are made only to other responsible agents, and in a deterministic world there aren't any other responsible agents.)

Anyway, I don't think your view falls prey to the modal problem.

But what I'd really like to hear from you about is what you'd say about the sentence: "I know it's not true that Jones will mow the lawn tomorrow, but I know (or at least have overall very strong evidence) that Jones will mow the lawn tomorrow." (Think of the case where you have extremely strong inductive evidence that he will. Then you know, or at least have overall very strong evidence, that he will. But if you know your theory to be right, then you also know that it's not true that he will.) It sounds odd, especially with the two "knows". (One can't rule this out by saying that to believe p requires one to believe that true(p), since we don't want that regress.)

Alex: I'm not Keith, but I hold a lot of similar views, so I'll take a stab at it (I'm currently working on a dissertation chapter on this, so figured I'd jump in).

You give the conjunctive sentence: "I know it's not true that Jones will mow the lawn tomorrow, but I know (or at least have overall very strong evidence) that Jones will mow the lawn tomorrow."

To clarify, its first conjunct seems misleading because incomplete: it needs to be "I know it's not (now) true *and not false* that Jones will mow the lawn tomorrow."

As for the second conjunct, since most everyone agrees that knowledge is factive, the second conjunct can't, for the open futurist, be "I know that...", since it's not yet true. So for any future-directed case, the most that the open futurist can claim is "strong inductive grounds" that don't amount to knowledge. (Some theories of knowledge allow for future-directed knowledge (eg Goldman 1967, repr. 1992: pp. 75-6, and Roush 2005: 114f.). But its not clear that the open futurist would agree...)

Now Keith can set straight what I've said...

"I know it's not true that Jones will mow the lawn tomorrow, but I know (or at least have overall very strong evidence) that Jones will mow the lawn tomorrow."

Bringing in knowledge makes things a mess for me. (I actually have spent time thinking about whether 'knows' is strongly or weakly factive in your senses [and was leaning toward weakly] and a lot of connected issues, which I haven't gotten a good line on yet.) So going with the "at least have overall very strong evidence" reading -- or perhaps shortening that by just using "probably" in some suitably epistemic way, yields strange-sounding conjunctions I'm led to endorse:

"It's not true that Jones will mow the lawn tomorrow, but he probably will mow the lawn tomorrow."

Things to appeal to in helping that go down: Following Matt's comment, it doesn't sound as bad with "now" inserted, esp. if "nor false" is also inserted: "It's not NOW true NOR FALSE that Jones will mow the lawn tomorrow, but he probably will" sounds fine to me. It's also worth pointing that (I'm pretty sure) the position can comfortably include that it PROBABLY WILL BE TRUE that Jones mows the lawn tomorrow. Won't go through the details of how to use those things in mitigating the intuitive damage, but I think the prospects are pretty good.

Alex: I take it you mean that the p you're working with is that Jones will freely mow the lawn *tomorrow* or at some future time t.

You say "But, plausibly if x believes p on extremely good evidence, *and p,* and it's not a Gettier case, then xKp. So, M(xKp)."

But why do you get to add the "and p" ? The open futurist thinks such a p is ntnf. So to say "and p" doesn't make a lot of sense to me: what is it for p to "be" if p is ntnf?

This is perhaps a roundabout way of saying that I don't really understand your axiom 1, that If p, then Tp. If "p" just *means* "Tp" then I can accept it, but that's not what's supposed to mean, right? Here's another worry about axiom 1: it's compatible with (If p, then Tp) that (~p & Tp). But that just sounds crazy. Of course, axiom 2 takes care of that problem, but then why not endorse only it?

The sentence you should deploy is, I think, not one of the form K(p) & K(~Tp), as you do several times above, but rather

"Jones will mow tomorrow, but it's not true (yet) that Jones will mow tomorrow." This version doesn't contain "I know". And it has the feeling of opposition to axiom 1, since it amounts to (p & ~Tp). But as Keith has suggested, the open futurist can say that any acceptable utterance of this kind will be acceptable only on the probabilistic reading of its first conjunct (ie, it's elliptical for "Jones PROBABLY will mow tomorrow").

Alex: re: your last post - (i) knowledge is not (and I think Keith would agree) the norm for *future* tensed assertion, and that's enough to handle a case like this. But additionally, (ii) the reason why "Probably p" sounds too weak in the case given is arguably because what happens to your shoes through tomorrow is something over which you have a great deal of control. And in most cases uttering "Probably p" is infelicitous-because-too-weak when p concerns something under your control: it's typically felicitous only when the utterer means to imply that s/he hasn't made up her/his mind yet. Due to this, saying "Probably p" when one is in a position to say "p" is misleading, and it violates the "Assert the Stronger" rule. And we usually grant that when it concerns your own decisions (like about what to do with your shoes) you are in a position to assert the stronger "p".

I was thinking that using "probably" would help the objection, because it's shorter than the "I have overall very strong evidence for" formulation you suggested. (The tension in a conjunction can be dissipated by lot of words, especially if they're a little techy, as opposed to being very common.) But if there's a worry that "probably" is too weak, we can go with the longer formulation. Just as I reported that

"It's not now true nor false that Jones will mow the lawn tomorrow, but he probably will"

sounds fine to, so does

"It's not now true nor false that Jones will mow the lawn tomorrow, but I have overall very strong evidence that he will"

If you get rid of anything else and make one of the conjuncts be simply "he will [mow the lawn tomorrow]," you raise the complication that in flat-out asserting that he will, the speaker may be representing herself as knowing that.

Hmmm... Alex, maybe it's just me, but I find it hard to swallow the idea that you "surely know p1" based merely on evidence concerning PvI's character + travel to the South Pole being "hard to arrange"... If that's all you're going on, then I don't think you know it (though if you have some other evidence about PvI's whereabouts, then perhaps you do know it).

I'm also suspicious of the idea that you're better positioned with respect to p2 than p1 just based on it being an "order of magnitude more out of character" (whatever that means when we're dealing with an individual's character)... That strikes me as reminiscient of Bob Adams' 1977 "Middle Knowledge" paper discussion of whether God can know what Saul will freely do based on knowing Saul's character. But if God can't know what Saul will do, why think that you can know what PvI will do? (Perhaps you don't buy Bob's argument...?)

Alex: I'm fully aware of the probabilistic or statistical nature of our epistemic grounds. I'm also fully aware that it can't be the whole story, or else then we would know that a given lottery ticket won't win, when the lottery gets large enough... but we don't know that.

My point was that the inductive grounds you give for your p1 aren't good enough for knowledge. And also, that given those, your inductive grounds for p2 aren't good enough either, since it's based on the exact same inductive background, and especially given that p2 was supposed to be, by hypothesis, ntnf (yet). So I'm not convinced that your pair p1 and p2 has shown us anything.

Alex: Oh. Well it appears you're in the minority re: 1.

2. I don't think you know that it's not a fake, but I do think you can come to know that your paper has been accepted by way of the letter + your inductive background regarding such letters - although no one gets journal acceptance letters (hardcopy) anymore, do they? :)

But that case differs from your p1 or p2: in this case you have positive evidence concerning your paper that fits your background about such matters... Whereas in your p1 and p2 cases, you didn't have any positive evidence concerning p1 or p2: all you had was a bit of inductive background about travel and PvI's character.

3. Not sure about this one. I think one would fail to know the thing about Al purely because it's ntnf; but even leaving that aside, I'd have to say that *I* don't know he won't be elected, because I don't have the requisite grasp of the Russian political process! - so I don't have the relevant inductive resources to say... For someone who does, they might be in a strong enough epistemic position that we'd plausibly count them as knowing...

Hmm. For some reason, one of my comments that was on this thread has disappeared. I did save it, so I can re-post it. The below comment is supposed to be right before Alex's comment of March 2, 2009 5:11 PM

*********
Sorry to have tuned out, Alex -- Just a sudden crush of busy-ness. I'm not sure I'm understanding your modal worry correctly. I think the sense in which "future contingents" are being said to be "contingent" is that there are causally possible (or something like that: terminology varies) futures in which they're true & also causally possible futures in which they're false. The open futurist -- or at least the OF of my basic stripe -- says that in such cases the future-directed propositions in question are ntnf. That doesn't sound like the kind of thing which will itself be a contingent truth, so I guess I'm inclined toward these:

It's metaphysically necessary that if p is a FC [where this is spelled out as above, in terms of causal possibility] at t, then p is ntnf at t

It's metaphysically impossible that p is a FC at t, but is either true or false at t.

*Keith will shovel his driveway Monday afternoon* is now a FC. But the "semanticized" version of it, *It is true [now: 11:38 am Monday morning] that Keith will shovel his driveway Monday afternoon*, is not a FC: there are no causally possible futures (relative to now) at which it is now true that I shovel on Monday afternoon. It's now inevitable that the latter "semanticized" proposition is true, but it's not now inevitable that I will shovel -- or that I won't (no matter what my wife says). I'm not sure how well that responds to your modal worry.

There's a lot of terminology that can be moving around. I construe propositions as having times built into them. If you think of *Keith is wearing a hat* as something that is true at some times and false at others, then I won't count it as a proposition, but as a "proposition frame" (or whatever terminology one wants to use here). *Keith is wearing a hat at 11:53 am, March 2, 2009* is a proposition (and may well be what's expressed now by the sentence "Keith is wearing a hat"), as is *Keith is wearing a hat at some time on March 2, 2009*. I don't know how many others I speak for, but when thinking of propositions in such terms, I don't believe they can switch truth-values (they can't change from true to false or from false to true), or lose truth-values, but they can gain a truth value: they can go from ntnf to True or from ntnf to False.

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